
==== Front
Heliyon
Heliyon
Heliyon
2405-8440
Elsevier

S2405-8440(24)11202-9
10.1016/j.heliyon.2024.e35171
e35171
Research Article
Exergy, exergoeconomic optimization and exergoenvironmental analysis of a hybrid solar, wind, and marine energy power system: A strategy for carbon-free electrical production
Zainul Rahadian abmn
Basem Ali c
J. Alfaker Mohamad d
Sharma Pawan ef
Kumar Abhishek abhikumar.shobhit@gmail.com
gh∗∗
Al-Bahrani Mohammed i
Elawady A. l
Abbas Mohamed j
Fooladi Hadi asd941734@gmail.com
l∗
Pandey Shatrudhan k
a Department of Chemistry, Faculty of Mathematics and Natural Sciences, Universitas Negeri Padang, Indonesia
b Center for Advanced Material Processing, Artificial Intelligence, and Biophysics Informatics ‌(CAMPBIOTICS), Universitas Negeri Padang, Indonesia
c Faculty of Engineering, Warith Al-Anbiyaa University, Karbala, 56001, Iraq
d Department of Petroleum Engineering, Al-Amarah University College, Maysan, Iraq
e Department of Chemistry, School of Sciences, Jain (Deemed-to-be) University, Bengaluru, Karnataka, 560069, India
f Department of Sciences, Vivekananda Global University, Jaipur, Rajasthan, 303012, India
g - School of Pharmacy-Adarsh Vijendra Institute of Pharmaceutical Sciences, Shobhit University, Gangoh, Uttar Pradesh, 247341, India
h Department of Pharmacy, Arka Jain University, Jamshedpur, Jharkhand, 831001, India
i Chemical Engineering and Petroleum Industries Department, Al-Mustaqbal University, Babylon, 51001, Iraq
j Electrical Engineering Department, College of Engineering, King Khalid University, Abha, 61421, Saudi Arabia
k Department of Production and Industrial Engineering, Birla Institute of Technology, Mesra, Ranchi, 835215, India
l - Independent Researcher, India
m Research Fellow, INTI International University, 71800, Nilai, Negeri Sembilan, Malaysia
n Professor Fellow, Superior University, Lahore, Pakistan
∗ corresponding author asd941734@gmail.com
∗∗ corresponding author abhikumar.shobhit@gmail.com
03 8 2024
30 8 2024
03 8 2024
10 16 e3517110 11 2023
19 7 2024
24 7 2024
© 2024 Published by Elsevier Ltd.
2024

https://creativecommons.org/licenses/by-nc-nd/4.0/ This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
In this research, aligned with global policies aimed at reducing CO2 emissions from traditional power plants, we developed a holistic energy system utilizing solar, wind, and ocean thermal energy sources, tailored to regions optimal for ocean thermal energy conversion (OTEC). The selected site, characterized by favorable wind and solar conditions close to areas with high OTEC potential, is designed to meet the electricity needs of a coastal community. The system's core components include an Organic Rankine Cycle, turbines, thermoelectric elements, pumps, a heat exchanger, a wind turbine, and a solar collector. A detailed system analysis and thermodynamic evaluation based on thermodynamic principles were carried out using the Engineering Equation Solver (EES) software. Key factors such as wind speed, solar radiation, and collector area were critical in determining system performance. To enhance the system's effectiveness, we conducted a comprehensive comparison of optimization algorithms, incorporating the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and utilizing a Pareto front for value optimization. This approach significantly outperformed other algorithms such as Particle Swarm Optimization (PSO), Genetic Algorithm (GA), and Simulated Annealing (SA) in terms of system efficiency and cost-effectiveness. The developed system achieved an exergy efficiency of 14.46 % and a cost rate of $74.98 per hour, demonstrating its suitability for its intended functions. Moreover, exergoenvironmental evaluation was conducted for the proposed plant. The findings revealed that key component HEX has a high exergoenvironmental factor due to their use of hot water, which has zero unit exergoenvironmental impact. Additionally, pumps demonstrated a zero exergoenvironmental impact factor, indicating negligible component-related environmental impacts. Sensitivity analysis further evaluated critical performance parameters, revealing that increases in solar irradiation lead to decreased total system cost rates, while higher turbine temperatures resulted in a remarkable 14.08 % reduction in the system's cost rate. These results underscore the economic viability of operating the system at higher temperatures and strengthen the argument for its adoption from a financial perspective.

Keywords

Power plant
Solar energy
Wind power
Ocean heat energy
Exergoeconomic
Exergoenvironmental
Optimization
==== Body
pmc Nomenclature

Ap	Collector area (m2)	
CP	Specific heat at constant pressure	
FR	Heat removal coefficient	
Gb	Beam solar irradiance (W/m2)	
m˙	Mass flow rate (kg/s)	
P	Pressure (MPa)	
PP	Pinch point (°C)	
T	Temperature (°C)	
UL	Thermal loss coefficient	
x	Quality	
Z˙	Cost rate ($/h)	
Greek symbols	
ηpump	Pump efficiency	
ηturbine	Turbine efficiency	
Subscripts	
0	Ambient	
Eva	evaporator	
ex	exergy	
Abbreviations	
HEX	Heat Exchanger	
ORC	Organic Rankine Cycle	
PTC	Parabolic Trough Collector	
TEG	Thermoelectric Generator	

1 Introduction

In today's world, the pressing need to construct power generation systems that are affordable, reliable, sustainable, and secure has intensified due to the surging global energy demand linked to surging populations and elevated living standards [1,2]. The prevalence of renewable resources, such as solar, wind, and ocean thermal energy, has engrossed researchers' attention and confidence [3,4]. As a result, professionals have been actively exploring and exploiting these sustainable resources [[5], [6], [7]]. The transition from fossil fuels to clean and renewable energy sources is essential in the modern world [8]. To ensure the sustainability of future energy systems, more efficient energy mechanisms and increased utilization of renewable resources are required [9,10]. Moreover, with the growing incorporation of renewable energies in hybrid systems and cycles, it is critical to investigate the underlying factors and conditions that govern them [11,12]. This is indispensable to enhance their efficiency and optimize them inherently [13,14].

In their 2019 study, Khosravi and associates [15] assessed the synergistic potential of integrating an ocean thermal energy conversion (OTEC) cycle with a solar photovoltaic setup aimed at the co-generation of hydrogen and electricity in an economical and thermodynamic manner. Their research indicated that the utilization of ammonia (refrigerant 717) in the organic Rankine cycle could achieve an output of 20.3622 kW/m2. Additionally, it was ascertained that the combined OTEC system could attain a maximum net electricity production efficiency of 3.318 %, considering the overall energy efficiency of the plant. Preceding this, Wang et al. [16] in 2018, explored the multi-objective optimization and efficacy of an OTEC plant employing the organic Rankine cycle. They identified refrigerants R 601 and R 601A as the most exergy efficient among the candidates, with R600 also noted for its performance. Advancing this field, Hassan and Dincer [17] in 2020, introduced an innovative renewable energy system leveraging ocean thermal energy. Its purpose was for cooling, ammonia production, and electricity generation. Simultaneously, Liu et al. [18] presented a comprehensive review of previous research concentrating on closed thermodynamic cycles of ocean thermal energy conversion. Their analysis explored thermodynamic cycles that operate with either pure or mixed fluids, with consideration to the impact of diverse fluids on overall cycle efficiency. The study's findings indicate that selecting the appropriate working fluid and implementing strategies to increase thermal energy yield from oceans can lead to optimal thermodynamic efficiency. Moreover, Qureshi and Dincer [19] conducted an analysis of an innovative system utilizing renewable solar energy for hydrogen production. The energy and exergy efficiencies of 25.07 % and 31.01 % were determined in the developed plant, respectively. Besides, due to promising results reported in that paper, the authors emphasized on the potential of the system to contribute to sustainable energy production. Additionally, the solar receiver exhibited exergy destruction and power production values of 115.86 MW and 388.80 kW/kg, respectively. Additionally, it was emphasized that the receiver exhibited the highest rate of heat transfer.

Ishak and Dinser [20] conducted a comparative analysis of renewable systems that utilize ocean thermal energy. The research covered Cu–Cl solar and wind energy systems, along with a thermochemical cycle. The study specifically concentrated on systems designed for hydrogen production. The potential of OTEC systems was highlighted as a highly effective means for renewable hydrogen production by their investigation. In Ref. [21], researchers conducted a study analysing the thermodynamics of a complex system that integrates solar and biomass energy to produce hydrogen. The system included an electrolyzer for hydrogen production, a thermal solar energy unit, a gas conversion component, a Rankine cycle, and a gas turbine. Technical terms were explained upon first use and a clear logical structure was maintained throughout. The investigation revealed a distinct trend: heightened pressure within the compressor and elevated photovoltaic-thermal (PV/T) values were directly proportional to an increase in both exergy destruction and system costs, which in turn inversely affected the exergy efficiency. Energy storage is a necessary option in the renewable-driven energy systems [22,23]. In a related inquiry, Razmi et al. [24] scrutinized a centralized energy system that amalgamated compressed air energy storage, an organic Rankine cycle, and a vapour-compression refrigeration cycle. Their findings underscored the critical importance of implementing an apt energy management strategy for the system in question, establishing it as a critical prerequisite for ensuring a financially viable investment return.

Ali Rahmi and colleagues [25] performed an exhaustive analysis of the energy, exergy, and economic dimensions, along with the multi-objective optimization, of an intricate energy system. Their research was directed towards optimizing the production of hydrogen, freshwater, cooling, heating, hot water, and electricity by integrating exergy and total cost as the primary objective functions for optimization. A genetic algorithm was utilized to facilitate this optimization. A miltigeneration system was developed in Ref. [26]. Concurrently, Wu et al. [27] focused on the thermodynamic enhancement of a marine thermal energy conversion system featuring a dual-pressure organic Rankine cycle, with the goal of augmenting the exploitation of marine thermal energy. Their findings indicated a marked enhancement in the net power yield post-optimization. In another pertinent study, researchers [28] executed a comprehensive evaluation of an integrated system designed for simultaneous cooling, desalination, and power generation. They meticulously analyzed both energy and economic factors, ensuring that technical terms were defined upon their initial use, and maintained an objective and impartial narrative throughout the study. Their findings introduced an innovative system adept at concurrent production of cooling, freshwater, and energy through the incorporation of ejector refrigeration cycle subsystems. Their research concluded that the system could potentially realize maximum energy savings of 33.72 % and exergy efficiencies of 29.33 %.

Yilmaz et al. [29] developed a clean and sustainable hybrid plant under a renewable energy-based hydrogen generation plan. They conducted the energy and exergy analysis to determine the system performance. Further, the hydrogen liquefaction unit was integrated to storage. Total energy and exergy efficiency was computed as around 32.8 % and 50.1 %, respectively. Utilizing solar energy as the driving power of energy systems has been widely implemented in literature. For example, in Ref. [30], scholars explored a novel solar-based energy system with thermal storage is analyzed through two case studies, examined under different energy outputs and efficiencies. The first case study, focusing solely on electricity production, achieves energy and exergy efficiencies of 31.66 % and 33.36 %, respectively. The second case study, which integrates electricity, heat, cooling, hydrogen, and water production, records efficiencies of 20.68 % and 16.87 %, alongside substantial daily hydrogen and clean water production. These findings underscore the system's capability to meet community energy needs in a sustainable manner. Hao et al. [31] developed an advanced solar-driven supercritical carbon dioxide-heat pump cogeneration system introduced, and analyzed using the heat current method for exergy evaluation. A significant exergy loss, primarily in the solar energy conversion component, was identified, with the system achieving an exergy efficiency of 34.69 % under rated conditions. Variations in direct normal irradiance and other operational parameters' effects on the system's performance were explored, indicating sensitivity to changing conditions. The potential for enhanced cascade energy utilization through this integrated system was highlighted. Moreover, in another similar study, Abur Houran et al. [32] integrated Parabolic Trough Solar Collectors (PTC) with Photovoltaic (PV) modules and Organic Rankine Cycles (ORC) and examined it based on energy and exergy efficiencies through three-dimensional simulations. It is found that the PTC-PV-ORC configuration exhibits the highest electrical performance, especially under low solar flux, achieving an energy efficiency of 21.46 % and an exergy efficiency of 13.33 %. Conversely, the PTC-PV system shows optimal exergy performance at 14.31 %. These findings propose enhanced performance methods for traditional solar thermal units through innovative integration techniques.

Moreover, the mechanical or thermal potential of other sources, such as wind and geothermal energies, has also been taken into account by experts and scientists. For instance, in Ref. [33], scholars examined a novel wind-driven poly-generation system that integrates various components like alkaline electrolyzers and fuel cells to optimize energy use. By analysing the effects of key parameters on exergy efficiency, it found significant gains, notably a rise to 58.83 % in overall system efficiency with increased fuel cell operating temperatures. The system demonstrates economic viability with a static payback period of 7.3 years and the potential for increased annual revenue through effective waste heat utilization. Enhancing conditions such as electrolyzer temperature and hydrogen storage pressure markedly improves performance. Kelem and Yilmaz [34] developed a multi-generation plant powered by geothermal energy, focusing on the production of power, hydrogen, hot water, freshwater, and drying capabilities. The integration of a flash-geothermal cycle, a Transcritical CO2 fluid Rankine cycle, a dryer, and a multi-effect desalination unit was examined. Significant enhancements in energy and exergy efficiencies were achieved, supporting the plant's sustainability and potential to contribute to net-zero emissions goals. The findings emphasized geothermal-supported systems' environmental and efficiency benefits in addressing global warming and environmental challenges.

On the other hand, the integration of different energy resources has been identified as an alluring option for improving the efficiency of the proposed systems. In this regard, Ghasemi et al. [35] developed a multi-generation energy system combining solar and biomass resources to generate various forms of energy, including electricity, heat, cooling, LNG, and freshwater. Through detailed thermodynamic and economic evaluations, along with advanced optimization techniques like Genetic Algorithms, the system reached energy and exergy efficiencies of 46.8 % and 11.2 %, respectively. Further analysis through sensitivity testing and optimization helped improve these metrics to an exergy efficiency of 9.9 % with a cost reduction of $13.32 per hour. The study underscored the benefits of integrating multiple energy processes to optimize the use and efficiency of renewable resources.

In our study, we developed an innovative energy system powered by the integration of solar, ocean thermal, and wind energies. Designed for specific climatic zones near high-potential areas for technological deployment, this system is tailored to fulfil the daily energy requirements of a typical coastal service provider. The system's architecture includes several key subsystems and novelties:- Flat Plate Solar Collector: This subsystem captures solar energy throughout the day, providing a reliable source of heat and electricity.

- Ocean Thermal Energy Conversion Unit: Utilizes temperature differences between surface water and deeper cold water to generate electricity, using water as the effective transfer medium.

- Wind Turbine: Converts kinetic energy from wind into mechanical energy, which is then converted to electrical energy, contributing significantly to the system's power output [36].

- ORC: Employs R227ea, a hydrofluorocarbon refrigerant, as the working fluid to efficiently convert collected thermal energy into mechanical power, enhancing overall system efficiency.

- Thermoelectric Generator: Directly converts heat differences into electricity using the Seebeck effect, optimizing energy usage and reducing waste.

To model the system and evaluate thermodynamic properties, we used the EES software. Furthermore, we applied a sophisticated multi-objective genetic algorithm to enhance and optimize system performance, specifically the NSGA-II. This tool was instrumental in:- Optimizing Objective Functions: Fine-tuning the system's operational parameters to achieve maximum efficiency and sustainability.

- Pareto Frontier Demonstration: Illustrating the trade-offs between competing objectives, such as cost versus efficiency, to identify the most effective solutions without compromising on other crucial performance metrics.

This detailed approach not only ensures that our energy system efficiently meets the varied demands of coastal service providers but also highlights the novelty of integrating wind, solar, and ocean thermal energy sources. Additionally, designing this system specifically for off-grid coastal areas represents another innovative aspect of our research, promoting environmental sustainability through intelligent energy management in regions traditionally underserved by conventional power grids. To recapitulate, recent advancements in renewable energy systems underscore the potential of integrating multiple energy sources to enhance both efficiency and sustainability. Our study introduces a novel approach by integrating solar, wind, and OTEC systems, specifically tailored for coastal communities. This focus on synergistic integration, designed to leverage the unique geographic and environmental characteristics of coastal areas, distinguishes our research from the prevailing literature. Unlike previous studies that often examine isolated systems or limited combinations, our research delves into the synergistic effects of integrating solar, wind, and ocean thermal energies. This architecture is meticulously designed for coastal regions, which are ideally positioned to harness these combined energy resources due to their inherent environmental features. Our study includes a detailed exergoeconomic assessment and exergoenvironmental beyond traditional exergy analysis. This dual perspective is vital for evaluating the integrated system's energy efficiency, economic viability and environmental impacts, providing critical insights for practical implementation. The design of our system is specifically tailored to the climatic conditions of the selected site, ensuring the optimal utilization of available renewable resources. This site-specific strategy enhances efficiency and is often neglected in broader studies.

Additionally, to substantiate the optimization strategy employed in our system design, we conducted a comparative analysis of various optimization algorithms, including the NSGA-II, PSO, GA, and SA. This rigorous comparison demonstrates that NSGA-II offers superior performance in optimizing the intricate balance between operational efficiency and cost-effectiveness, further distinguishing our approach [37]. Our study transcends typical case studies by comprehensively examining the integration of these three renewable energy sources for specific locales. This method serves as a foundational model for future implementations and research in analogous environments. The manuscript has been developed to reflect these significant enhancements, clearly articulating the study's innovative contributions and its relevance to contemporary energy challenges.

2 System description

The energy system described in this study aims to generate electricity in a coastal town using renewable sources such as sun, wind, and ocean energy. Fig. 1 illustrates the configuration and diagram of the analyzed energy system. The provided energy system incorporates an organic Rankine cycle (ORC), wind turbines, a flat plate solar collector-driven thermal solar unit, and a thermoelectric generator (TEG). In addition, many peripheral components, including pumps, steam turbines, electrical converters, and pipes, were integrated into the energy system. Three distinct units, namely a wind turbine, an ORC system, and a TEG device, have been utilized to generate electrical energy. Solar energy and ocean energies are sources of thermal energy utilized in the process.Fig. 1 Schematic of proposed CO2-free integrated power plant.

Fig. 1

Wind turbines immediately transform the kinetic energy of wind into electrical energy. The wind farm harnesses energy from the wind and transfers it to the grid using an electrical converter. Conversely, the steam turbine in the ORC unit generates electricity by harnessing thermal energy from the heat exchanger via a Rankine cycle. An Organic Rankine Cycle (ORC) is a type of Rankine cycle that use an organic fluid instead of water to enhance the efficiency of the power production process. The solar field provides the necessary heat duty for the heat exchanger. The solar field under consideration utilizes flat plate solar collectors. These solar collectors can generate the necessary heat for the ORC unit by absorbing solar energy and transferring it to the working fluid. Thermoelectric generators, capable of generating electrical energy from low-quality energy sources, collect heat from the heat exchanger and the outlet of the steam turbine. TEGs convert waste heat into useable power by utilizing a heat source and a cold reservoir. They are well-suited for isolated areas that lack access to public utilities but have a readily available heat source. In this context, ocean water is seen as a cold reservoir for the Thermoelectric Generator (TEG). The power generated by the ORC (Organic Rankine Cycle) and TEG (Thermoelectric Generator) is transferred to the electrical grid using an electrical converter. Hence, the suggested energy system has the capability to produce electrical energy through an environmentally sustainable procedure. The pumps are powered by the energy system, which supplies the electrical energy required for their operation. This research explores the conceptual design, thermodynamic analysis, cost feasibility, and optimization of the proposed energy system.

3 Exergoeconomic modelling of proposed plant

In this section, the modelling criteria of the proposed system based on energetic and exergoeconomic points of view are scrutinized.

3.1 Modelling of solar collector

Flat plate solar collectors are a widely utilized technology for converting solar energy into useable thermal energy [38,39]. They consist of a flat-plate absorber, transparent cover(s), a heat-insulating backing, and a fluid that carries heat away from the absorber. The absorber captures solar radiation, converts it into heat, and transfers this heat to the fluid passing through channels or tubes attached to the absorber.

In this study, based on the features of the selected collector, the heat flux of working fluid is calculated by Eq. (1) [40,41]:(1) Qwf˙=m˙Cp(T10−T9)

In above equation, T10 denotes the outlet stream of collector (point 10), while the inlet stream of the collector has been pointed out by T9. In equation (1), the specific heat constants for constant pressure has been shown by Cp. Also, m˙, is mass flow rate of solar collector.

The useful heat Qu collected by a flat plate collector can be calculated by considering the thermal losses of the collector using the Hottel-Whillier equation as Eq. (2) [31,42]:(2) Qu=Ac×(G×ω0−U×(Tin−Tout))

where, Ac is the area of the collector exposed to sunlight (m2), G the intensity of solar radiation reaching the collector(w/m2). Moreover, the thermal efficiency under standard conditions (G equal to 1000) has been denoted by ω0 , and U the overall heat transfer coefficient of the collector. Accordingly, the thermal efficiency of the solar collector is estimated by Eq. (3) [43]:(3) ηc=QuG.Ac

Here, the efficiency of the solar collector is considered to be 50 %.

3.2 Modelling of thermoelectric

Thermoelectric refers to a type of heat engine devoid of moving parts, wherein electrons function as the working fluid, converting heat to electricity. These generators have a lower mass-to-power production ratio compared to other energy production methods and, due to the absence of moving parts, exhibit high reliability and require less maintenance. For thermoelectric analysis, the calculation of thermoelectric efficiency in this system employs the following relationship [44]:(4) ηTEG=ηcarnot×(((1+ZTM−1)(1+ZTM+(TcoldTHot))

where, ZTM is the figure of merit of thermoelectric material. In this study, the value of this parameter has set on 0.8. The ability of a material to generate thermoelectric power is associated with the figure of merit, which is a dimensionless parameter.

3.3 Modelling of wind turbine

Wind turbines convert the kinetic energy of wind into electrical power through a complex interplay of aerodynamic, mechanical, and electrical processes. A typical model of a wind turbine begins with the characterization of the wind resource, followed by the application of the Blade Element Momentum theory to calculate the forces on the turbine blades. The rotational motion induced in the turbine's rotor is then translated into electrical energy via a generator, the performance of which is defined by its power relationship between wind speed and electrical output. In this investigation, the area of wind turbine is measured by Eq. (5) [45]:(5) AWT=(D2)×(π4)

The electricity generated from a wind turbine is calculated by considering the maximum wind speed and the typical wind speed, which can be expressed in terms of the total work of the ORC cycle as Eq. (6) [45]:(6) W˙WT=((12)×(ηWT×AWT×ηecoefficiency×VAv,Wind3((41000))

3.4 Performance assessment of proposed plant

In this investigation, to asset the performance of the proposed CO2-free power plant, net power output, the investment cost return and product cost rate are considered. In this regard, the net power output of the proposed plant that includes generated power of ORC sub-cycle, the wind turbine and the thermoelectric are calculated as Eq. (7) [45]:(7) W˙net=W˙ORCsub−cycle+W˙WindTurbine+W˙TEG

Exergy is defined as the maximum work that can be obtained by a system or a material flow as it reaches equilibrium with a reference environment [[46], [47], [48]]. The amount of exergy destruction of the entire system is calculated using the following relationship [47]:(8) Ex˙Total=Ex˙SolarCollector+Ex˙Turbine+Ex˙TEG+Ex˙WindTurbine+Ex˙Pump1+Ex˙Pump2+Ex˙Evaporator

The net cost rate of the plant is calculated by Eq. (9) [49]:(9) ZTotal=ZSolarCollector+ZTurbine+ZTEG+ZWindTurbine+ZPump1+ZPump2+ZEvaporator

The capital recovery factor (CRF) is defined by Eq. (10) [50]:(10) CRF=(ix(1−α)m(1+α)m−1)

The profitability and the operational period of the power plant (in years) are indicated as α and m which are respectively 0.1 and 20.

Given that each component of a combined system is expected to operate at a specific time frame, the cost rate of each device serves as a good indicator of efficiency. The capital cost rate of each device is calculated using the following equation [49]:(11) Z˙k=Zk×CRF×ϑN

where, Z denotes the cost of plant's elements. Moreover, annual operation period (per hour) and the maintenance factor are denoted by N and ϑ, respectively. The input data for modelling of the proposed plant are listed in Table 1. Further, Table 2 gives the investment cost formulations for the components.Table 1 Input data for modelling of the proposed plant.

Table 1Input Parameter	Parameter Indicator	Value	
Ambient Temperature	T0 (°C)	25	
Ambient Pressure	P0 (kPa)	101.3	
Inlet Pressure of Solar Collector	P9 (kPa)	150	
Solar Collector Area	Ap (m2)	(800–1200)	
Sun Radiation Intensity	Gb (W/m2)	800	
Temperate of Ocean Water	T8 (°C)	30	
Outlet Temperate of Solar Collector	T10 (°C)	95	
Mass Flow Rate	m˙ (kg/s)	10	
Sun Surface Temperature	T Sun (K)	5770	

Table 2 The investment cost formulations for the components [11].

Table 2Component	Investment cost	Component	Investment cost	
Turbine	ZTurbine=4405×WTurbine0.7	TEG	ZTEG=1500×WTEG	
Solar collector	ZFPC=800×AFPC	Heat exchanger	ZHE=8300×WTurbine0.78	
Pump	ZPump=3540×WTurbine0.71			

3.5 Validation of modelling

To ensure the reliability and accuracy of the modelling performed, this section undertakes a comparative validation with a corresponding study referenced as [50]. The comparative results, focusing particularly on the thermoelectric performance of the model, are displayed in Fig. 2. It is clearly evident from the graphical representation that the simulation developed for this investigation exhibits a high degree of congruence with the outcomes reported in the cited reference. This alignment not only corroborates the methodologies employed but also reinforces the credibility of the simulation results obtained in the present work.Fig. 2 Validation of the proposed plant with similar study in Ref. [51].

Fig. 2

In addition, the validation of the solar collector (flat plate solar collector) model is based on the data and results reported in Refs. [43,52]. The comparative results for solar collector validation are given in Table 3. By comparing the results and the calculated maximum deviation, it can be concluded that the developed model for the solar collector has sufficient validity and can be used for the analysis of the proposed system.Table 3 Validation results of the solar collector model.

Table 3Parameter	Literature	Modelling	Deviation	
Inlet temperature	25 °C	25 °C	0.00 %	
Solar radiation	650 W/m2	650 W/m2	0.00 %	
Outlet temperature	31.3 °C	30.9 °C	1.30 %	
Thermal efficiency	25.4 %	25.1 %	1.2 %	

4 Exergoenvironmental evaluation of the proposed plant

When it comes to evaluating the process of energy conversion from a sustainability point of view, the exergoenvironmental study is regarded as a highly promising approach [53]. Exergoenvironmental analysis is a method that integrates thermodynamics and environmental science in order to assess the impact of environmental factors by applying the principles of thermodynamics. In a manner that is analogous to the manner in which costs are assigned to exergy streams in exergoeconomic analysis, exergoenvironmental assessment allocates the results of the environmental study to the exergy streams [40]. The results of the environmental study are subsequent turned into particular values through the processes of normalization and weighting, which ultimately results in a change in the influence of the system [41]. Using Eq. (12) [54], one may get the exergoenvironmental impact rate (B˙) of each stream. This rate is a representation of the overall influence that each stream has on human health, ecological quality, and resources.(12) B˙=bE˙X

where, the value of b represents the particular exergoenvironmental impact that each stream has. Equation (13) can be used to express the exergoenvironmental effect balance of each individual component that makes up the system [55]:(13) ∑B˙in,k+Y˙k=∑B˙out,k

where, Y˙k is the environmental impact rate of the kth component, wich can be defined as Eq. (14) [56]:(14) Y˙=Yhr×n

In this context, the annual operating hours of the system and the system life are denoted by the symbols hr and n, respectively. A component's environmental impact is denoted by the letter Y, and it can be calculated using Eq. (15) [55]:(15) Yk=∑iωi,k×Mi,k

The unit environmental impact of the product of the proposed plant is determined by following equation:(16) bp=B˙Wnet+B˙11+B˙7W˙net+E˙11+E˙7

Table 4 gives the developing exergoenvironmental equations for components of the proposed plant.Table 4 Developing exergoenvironmental equations for components of the proposed plant.

Table 4Components	Environmental impact balance equation	Auxiliary equation	
HEX	B˙10+B˙11+Y˙HEX=B˙3+B˙2	b10 = b3	
Turbine 1	B˙3+Y˙T=B˙4+B˙WT	b3 = b4	
Pump 1	B˙5+Y˙P1+B˙WP1=B˙6	–	
Pump 2	B˙8+Y˙P2+B˙WP2=B˙9	–	
Pump 3	B˙2+Y˙P6+B˙WP3=B˙1	–	
Thermoelectric	B˙1+B˙4+Y˙HEX=B˙6+B˙7	b1 = b7	
Solar Collector	B˙9+Y˙Val3=B˙1	–	

5 Result and discussion

This section is devoted to the presentation and critical discussion of the thermodynamic and exergoeconomic outcomes of the proposed energy facility. The assessment of the plant's operational efficacy involves a sensitivity analysis, where we scrutinize the repercussions of key input variables on performance metrics like exergy efficiency, the total cost rate of the product, the net power output of the thermoelectric component, and the net power output of the system as a whole. Subsequently, we employ a multi-objective optimization strategy to balance the trade-offs between exergy efficiency and the cost rate of the product, aiming to optimize the plant's performance economically and thermodynamically. Table 5 presents the thermodynamic properties of the plant's streams.Table 5 The thermodynamic properties of the plant's streams.

Table 5Point	T (°C)	P (kPa)	h (kJ/kg)	s (kJ/kg.K)	
1	30.0	200	1267.17	0.104	
2	30.0	500	1567.17	0.104	
3	180	580	2834.8	9.361	
4	100	101.3	1559.77	0.312	
5	30.0	101.3	125.73	0.474	
6	25.0	110.0	1246.27	0.088	
7	25.0	101.3	104.84	0.386	
8	30.0	101.3	125.73	0.474	
9	32.4	150.0	1275.53	0.111	
10	95.0	130	401.35	1.722	
11	30.9	101.3	129.49	0.490	

In order to substantiate the effectiveness and innovation of our integrated energy system, we conducted a comprehensive comparison of its general efficiency with findings from existing literature. The results of this comparative analysis are systematically presented in Table 6. This table illustrates key efficiency metrics, including exergetic and exergoeconomic assessments, for our system alongside those reported in similar studies. By juxtaposing these metrics, Table 6 provides a clear visual representation of how our system performs relative to other established systems in the field.Table 6 Efficiency and cost comparison of integrated energy systems across various studies.

Table 6Driving Energy Source	Exergetic Efficiency (%)	Cost Rate of Product ($/h)	Location	Ref.	
Multi-sources (solar& wind& ocean)	14.46 %	74.98	Coastal Area	This study	
Dual-sources (geothermal + solar)	23.18 %	175.1	Urban Area	[34]	
Dual-sources (biomass + solar)	15.16 %	13.32	Urban Area	[35]	
Dual-source (geothermal + solar)	60.59 %	32.22	Urban Area	[31]	

5.1 Sensitivity analysis

Sensitivity analysis involves a systematic approach to examining the potential impact of varying input parameters on a given output or set of outputs. By altering one variable at a time whilst holding others constant, we can establish the sensitivity of our results to changes in each input parameter. This technique provides informative insights into the resilience and dependability of a model's forecasts. Through the use of sensitivity analyses, it is possible to determine the parameters with the greatest influence on performance metrics. This provides valuable guidance for optimization efforts and decision-making processes. By comprehending the degree of sensitivity linked to each input, it is feasible to prioritize areas for further research, improvement, or control in the plant's design and operation.

5.1.1 Impact of pump isentropic efficiency on system's performance

The efficacy of “pump 2" within the system in question is crucial, directly affecting both the efficiency and the costs. This pump's efficiency is characterized by the ratio of the mechanical energy imparted to the working fluid against the electrical energy consumed. As illustrated in Fig. 3a, augmenting the efficiency of the pump from 0.7 to 0.8 yields a total system power enhancement of roughly 1.62 %. This enhancement translates to an increase in total power output from 360 kW to 365 kW. Concurrently, Fig. 3a elucidates that a rise in pump efficiency is also associated with a marginal gain in thermoelectric power of about 0.22 %, culminating in an increment in thermoelectric work from 108.05 kW to 108.28 kW. For modelling purposes, when the pump efficiency is set at 0.85, the total work registers a value of 364.642 kW, while the thermoelectric work is measured at 108.1403 kW for the same pump efficiency. It is important to note that achieving optimum pump efficiency is critical to ensuring that the fluid effectively reaches the intended point. Therefore, when selecting a pump, its duty point should be closely matched to its peak efficiency point to optimize pump performance.Fig. 3 The impact of pump's isentropic efficiency on the (a) net output power of the overall system and thermoelectric element and (b) exergy efficiency and product cost rate.

Fig. 3

Besides, as shown in Fig. 3b, there is a discernible correlation between pump efficiency and system exergy efficiency: an increase in pump efficiency results in an increase in system exergy efficiency of approximately 1.63 %. The underlying reason for this increase in exergy can be attributed to the direct relationship between the system's exergy and its work output. In essence, as the work output of the system increases, so does its exergy. From this relationship, it's clear that as exergy destruction decreases, efficiency increases proportionally. In addition, Fig. 3b illustrates that an increase in pump efficiency results in a 0.15 % decrease in expenditure, which is an economically significant implication.

5.1.2 Impact of turbine isentropic efficiency on system's performance

Fig. 4a demonstrates that improving the turbine efficiency from 0.7 to 0.95 leads to a significant increase in the total system work, from 342.334 kW to 386.861 kW, representing a hefty 13 % increase. The primary cause for this rise is the favorable impact of the turbine's efficiency on the output, as the turbine plays a pivotal role in the production of energy in these systems. Simultaneously, Fig. 4a demonstrates that an enhancement in turbine efficiency is associated with a 17 % reduction in thermoelectric effort. This phenomena can be explained by comprehending the concurrent functioning of the two subsystems accountable for power generation. Specifically, the thermoelectric generator's efficiency appears to rival that of the turbine when it comes to power generation. Additional potential factors that contribute to the decline in work include losses in production when machines are not active, degradation of thermoelectric performance due to unfavourable operating conditions (such as high temperatures, uncontrolled pressure, fluctuations in enthalpy, and growing inconsistencies within the subsystems). According to Fig. 4b, improving the efficiency of the turbine has a substantial impact on the overall exergy efficiency of the system. It results in a notable increase of 13.01 %. The observed association between the increase in exergy and the performance of the system demonstrates the direct connection between the exergy of the system and the amount of work it produces. Furthermore, Fig. 4b highlights the fact that an improvement in turbine efficiency is directly associated with a 1.61 % rise in the system cost ratio. One possible explanation for this pattern is the anticipated rise in system costs as a result of the increasing productivity, which necessitates the use of more large equipment. The analysis reveals that the higher cost ratio can be linked to the greater expenses related to solar and wind power generating. The primary reason for these exaggerated expenses is most likely attributed to the substantial financial investment necessary for energy generation, encompassing a range of equipment. Furthermore, the rising expenses of energy and the economic consequences of decreased productivity due to system downtime may also play a role.Fig. 4 The impact of the turbine's isentropic efficiency on the (a) net output power of the overall system and thermoelectric element and (b) exergy efficiency and product cost rate.

Fig. 4

5.1.3 Impact of steam turbine inlet temperature on system's performance

Fig. 5a delineates a discernible correlation between the turbine inlet temperature and the total work output of the system. It is observed that an elevation in the turbine inlet temperature corresponds with an enhancement in the system's total work output, quantified at a rise of 9.05 %.This is particularly interesting because one might expect a direct, consistent relationship between increased temperature and increased power. However, the data tells a more nuanced story. As the turbine temperature is systematically increased, there's a consistent upward trend in total work, but only up to a critical point of 56 °C. Beyond this temperature, an unexpected phenomenon occurs: total work begins to decrease significantly. This counterintuitive decrease is likely due to systemic overheating and the unique challenges a turbine faces when operating at high temperatures. At these elevated temperatures, components can experience thermal stress, lubrication can become less effective, and overall system efficiency can be compromised. Despite these challenges, it's important to note that the overall change in power output remains positive across the range of temperatures tested. In parallel, Fig. 5a also provides insight into the effect of turbine inlet temperature on thermoelectric work. Again, an initial increase in temperature corresponds to an 11.71 % increase in thermoelectric work. This positive trend continues until the turbine temperature reaches 54 °C. Beyond this temperature, however, the trend observed for the total work is mirrored: the thermoelectric work output begins to decrease. This decrease is mainly due to the negative effects of overheating on the thermoelectric generator. When exposed to temperatures beyond its optimal operating range, the generator may experience efficiency losses due to material limitations, reduced electron mobility, or potential thermal damage to its components. In summary, while increasing the turbine inlet temperature generally increases the work output of the system, there are inherent limitations and thresholds that must be considered to optimize performance and avoid detrimental effects.Fig. 5 The impact of steam turbine inlet temperature on the (a) net output power of overall system and thermoelectric element and (b) exergy efficiency and product cost rate.

Fig. 5

Fig. 5b presents the impact of variations in the turbine inlet temperature on the system's exergy efficiency. The trend demonstrated by the data indicates that a rise in the turbine inlet temperature enhances the exergy efficiency significantly, with an observed increase of 9.08 %. This upward trend in efficiency is maintained with the increase in temperature, reaching its zenith at a temperature of 56 °C. However, beyond this critical threshold, a reversal of the trend is observed: the exergy starts to decrease. A plausible explanation for this diminishing return after the 56 °C mark lies in the overheating of the system. Elevated temperatures can introduce certain operational challenges and inefficiencies. In addition, the system's ability to effectively convert energy may be compromised, which subsequently affects the overall efficiency of the system. This is particularly relevant given the sensitivity of system components to temperature fluctuations. Another interesting observation concerns exergy dissipation. A discernible increase in this metric could explain the observed drop in exergy beyond the optimum temperature. This escalation in exergy destruction is due to a disproportionate increase in output heat relative to the power required by the Rankine cycle turbine. In essence, “enhanced heat” refers to the optimal heat dissipation in the absorber. This heat, due to its elevated temperature, can potentially accentuate exergy destruction, thereby affecting the overall performance of the system. In addition, an economic perspective offered by Fig. 5b suggests a favorable financial impact. Specifically, as the turbine temperature increases, there's a remarkable 14.08 % reduction in the system's cost rate. This decrease not only underscores the economic viability of operating the system at higher temperatures, but also strengthens the argument for its adoption from a financial perspective.

5.1.4 Impact of solar collector's area on system's performance

Fig. 6a provides compelling insight into the profound influence of solar irradiance that is related to solar collector area on the operating performance of the entire system. A notable observation is that as solar collector area increases from 10,000 to 12,000 m2, the system's operating rate increases by a significant 13.94 %. The underlying mechanism for this increase can be traced back to the collector surface area. Essentially, there is a linear correlation between the area of the collector and its ability to capture solar energy. The larger the area of the collector, the greater the volume of solar radiation it captures. This increased capture, in turn, channels more energy into the system, thereby increasing its output. This relationship is further cemented by data showing that as the area of the solar thermal collector increases, the thermoelectric work rate increases by 16.12 %. Such an increase emphasizes the key role of the collector dimensions in optimizing the energy conversion efficiency of the system.Fig. 6 The impact solar collector's area on the (a) new output power of overall system and thermoelectric element and (b) exergy efficiency and product cost rate.

Fig. 6

Transitioning our focus to Fig. 6b unfolds a subtler aspect of the system dynamics, where an expansion in the solar thermal collector's area is correlated with a 1.88 % reduction in the total system exergy. This indicates that enlarging the collector's dimensions, although potentially beneficial for the work generation capacity, may simultaneously introduce certain inefficiencies that negatively affect the system's exergetic efficiency. On the economic front, the repercussions of augmenting the collector's size are more direct. The illustration in Fig. 6b delineates a 18.83 % surge in the overall system cost, which can be attributed to a confluence of factors. An increase in collector size inherently means more materials, which leads to a rise in maintenance, repair, and potential replacement frequencies. Moreover, the added complexity with a larger scale could necessitate more frequent start-ups, imposing additional stress and consequent wear on the system components. Such operational intricacies cumulatively amplify the cost framework of the energy system.

5.1.5 Impact of solar radiation intensity on system's performance

Solar radiation plays an indispensable role in determining the efficiency of systems equipped with solar thermal collectors. Its intensity directly affects the operation of these systems. Basically, as solar radiation increases, the flow rate of fluid into both the solar and wind subsystems increases. This increase in flow rate cascades into increased output from the subsystems, resulting in a proportional increase in the cumulative work output of the system. The reverse is also true a decrease in solar radiation causes in a decrement in proposed plant outcome.

Turning our attention to Fig. 7a, the effects of escalating solar irradiance become quite apparent. With an increase from 800 to 1000 W/m2, there's a striking 63.43 % increase in the system's work rate. Such a significant increase not only indicates superior performance but also points to a likely increase in the overall exergy of the system. Digging deeper into the specifics, Fig. 7a further shows that this increase in solar radiation boosts the thermoelectric work rate by an astounding 146.68 %. This is a commendable gain and underscores the direct relationship between solar radiation and thermoelectric work. As expected, this increase further increases the exergy of the entire system. However, Fig. 7b sheds light on another crucial dimension-exergy. Reflecting the increased work rate caused by the increased solar radiation, the exergy of the system experiences a 13.21 % increase. This suggests that as solar radiation increases, the system becomes more efficient at harvesting and utilizing energy. Finally, from an economic perspective, Fig. 7b presents an interesting observation. Despite the improved performance metrics, the total system cost rate decreases by 47.65 % as solar irradiation increases. This suggests that even though the system achieves better performance, its operational efficiency could result in significant cost rate savings.Fig. 7 The impact of solar radiation intensity on the (a) net output power of the overall system and thermoelectric element and (b) exergy efficiency and product cost rate.

Fig. 7

5.2 Results of exergoenvironmental analyses

Table 7 presents the exergoenvironmental metrics obtained from examining the proposed mechanism. When a unit's exergoenvironmental index exceeds 70 %, the main source of environmental damage comes from the impacts of individual components. On the other hand, indices below 30 % show that the primary cause of environmental harm is the destruction of exergy. HEX in the configuration is distinguished by a high exergoenvironmental index since it relies on hot water, which has minimal environmental impact, effectively eliminating any harm to the environment from exergy loss. Similarly, the pumps demonstrate a low exergoenvironmental impact factor, indicating that the environmental consequences caused by the components themselves are small compared to others.Table 7 Exergoenvironmental variables for each element of the proposed integrated plant.

Table 7Components	E˙x,Dk (kW)	B˙D (mPts/h)	Y˙k (mPts/h)	B˙D+Y˙k (mPts/h)	fb,k (%)	
Thermoelectric	510.2	31.0	0.55	31.55	1.75	
HEX	828.60	52.09	6.42	58.52	10.97	
Steam Turbine	750.25	48.5	11.0	59.5	18.5	
Pump 1	22.45	1.7	1.4	3.1	45.16	
Pump 2	21.3	1.65	0.85	2.5	34.0	
Pump 3	12.15	0.4	0.35	0.75	46.67	
Solar Collector	36.0	2.0	0.0	2.0	0.0	

5.3 Multi-objective optimization

To achieve the most efficient design of an energy system that yields the best possible results, optimization methodologies are indispensable. In the context of the multifaceted optimization challenges delineated in this study, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) was selected as the optimization tool of choice. Renowned for its prowess in identifying a broad spectrum of optimum solutions, NSGA-II is a cornerstone within the domain of multi-objective optimization. Introduced by K. Deb in 2002, this evolutionary algorithm stands out for its multi-objective optimization capabilities. It was designed as an advancement over its forerunner, the original NSGA, specifically to overcome certain limitations. NSGA-II harnesses evolutionary principles and genetic mechanisms to evolve and ascertain sets of optimal solutions, which are represented as Pareto fronts, indicative of the trade-offs between competing objectives.

Some notable features of NSGA-II include its Fast-Non-Dominated Sorting, the process by which solutions are categorized based on different levels of dominance. Solutions within the same front are said to be non-dominated with respect to each other. The Crowding Distance is a measure used to maintain solution diversity across the Pareto front. It calculates the density of solutions surrounding a given solution. Solutions with larger crowding distances are preferred because they are less dense and thus provide more diversity. In addition, NSGA-II incorporates elitism by directly propagating the best solutions from the current population to the next, ensuring that optimal solutions are not lost in subsequent generations.

For the purposes of this research, NSGA-II was implemented in two software platforms: MATLAB and EES. This dual software approach ensures robustness and flexibility to address the unique challenges of the research. For seamless integration between the two platforms and to facilitate multi-objective optimization, a dedicated code has been developed. This code acts as a bridge between the two software environments, enabling real-time data exchange and process communication.

In response to the necessity for a rigorous justification of the optimization algorithm employed, a comparative analysis was undertaken to assess the efficacy of NSGA-II against other prevalent algorithms, namely Particle Swarm Optimization (PSO), Genetic Algorithm (GA), and Simulated Annealing (SA). Each of these algorithms offers distinct mechanisms and advantages in the realm of optimization:- Particle Swarm Optimization (PSO): Mimics the social behaviour of birds flocking or fish schooling. It optimises a problem by iteratively improving a candidate solution with regard to a given measure of quality. It is known for its simplicity and ability to converge quickly to a good solution but can sometimes get trapped in local optima.

- Genetic Algorithm (GA): Based on the principles of natural selection and genetics. It uses crossover, mutation, and selection operations to evolve solutions towards an optimum. GA is highly effective for complex optimization problems but can be computationally intensive.

- Simulated Annealing (SA): Inspired by the annealing process in metallurgy. It explores the solution space by probabilistically accepting worse solutions to escape local optima. SA is particularly useful for problems with numerous local minima, although it may require careful tuning of parameters.

In this study, the design variables that are optimized using the DDE method have been listed in Table 8.Table 8 Design variables for multi-objective optimization propose and their changing values.

Table 8Design Parameter	Lower Value	Upper Value	
Ap (m2)	800	1200	
T@1 (°C)	15	30	
T@3 (°C)	40	60	
PPEvaporator (°C)	2.5	6.5	
ZTm (−)	0.5	1	
Pump's Efficiency (%)	0.7	0.9	
Turbine's Efficiency (%)	0.7	0.9	

Fig. 8 displays the Pareto-frontier of the proposed power plant. Further, the optimal objective functions and the optimal values of design variables are listed in Table 9, Table 10, respectively.Fig. 8 Pareto-frontier of the proposed power plant.

Fig. 8

Table 9 The optimal objective functions.

Table 9Objective function	Value	
Exergetic Efficiency (%)	14.47	
Cost Rate of Product ($/h)	74.97	

Table 10 The optimal values of design variables.

Table 10Design Parameter	Optimal Value	
Ap (m2)	8882.45	
T1 (°C)	16.56	
T3 (°C)	56.65	
PPEva (°C)	4.15	
ZTm (−)	0.72	
Efficiency of Pump (%)	0.8	
Efficiency of Turbine (%)	0.9	

The comparative analysis focused on two critical metrics: exergetic efficiency and the cost rate of production. NSGA-II demonstrated superior performance, delivering an exergetic efficiency advantage of 0.56 %, 0.46 %, and 0.86 % over PSO, GA, and SA, respectively. Furthermore, it achieved a reduction in cost rate of $1.52/h, $0.82/h, and $2.22/h compared to the aforementioned algorithms. These findings, illustrated in Fig. 9, substantiate NSGA-II's enhanced capability to optimize the system's operational and economic aspects. The decision to employ NSGA-II was thus predicated on its demonstrated superiority in handling the multi-objective optimization required for efficient and cost-effective energy system deployment. This selection is further validated by NSGA-II's robustness in navigating the complex solution space inherent in integrated renewable energy systems, ensuring a comprehensive alignment with the project's objectives. By elucidating the frameworks and comparative performance of these algorithms, the enhanced explanation underscores the rationale for selecting NSGA-II as the optimal tool for this study.Fig. 9 Comparative performance of NSGA-II versus PSO, GA, and SA in terms of exergetic efficiency and cost effectiveness.

Fig. 9

6 Conclusion

Given the urgent global need to transition to cleaner energy solutions, our research has undertaken a comprehensive exploration of a renewable energy system that utilizes solar, wind, and ocean thermal energy. This effort aligns with broader governmental policies aimed at reducing CO2 emissions from conventional power plants. Our proposed system is not merely theoretical; it is tailored for locations with optimal ocean thermal energy conversion potential, complemented by favorable wind and solar conditions.

The proposed plant, meticulously developed to address the power needs of coastal communities, incorporates a wide range of components, from the Organic Rankine Cycle and turbines to thermoelectric elements and solar collectors, each playing a critical role in energy harvesting and conversion. Using EES software, we conducted a comprehensive system analysis grounded in fundamental thermodynamic principles. Parameters such as wind speed, solar radiation, and collector area emerged as key factors affecting overall system performance.

In addition, optimization, a critical facet of our research, was approached with a blend of cutting-edge algorithms and traditional thermodynamic principles. The use of the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and the construction of a Pareto front proved instrumental in refining the system's performance metrics. The key findings from the current investigation are as follows:- The proposed system is specifically tailored for regions with optimal ocean thermal energy conversion potential, complemented by favorable wind and solar energy conditions.

- Despite the improved performance metrics, the total system cost rate decreases as solar irradiation increases. This suggests that even though the system achieves better performance, its operational efficiency could result in significant cost rate savings.

- As the turbine temperature increases, there's a remarkable 14.08 % reduction in the system's cost rate. This decrease not only underscores the economic viability of operating the system at higher temperatures but also strengthens the argument for its adoption from a financial perspective.

- An increase in collector size inherently means more materials, leading to a rise in maintenance, repair, and potential replacement frequencies. Moreover, the added complexity with a larger scale could necessitate more frequent start-ups, imposing additional stress and consequent wear on the system components. Such operational intricacies cumulatively amplify the cost framework of the energy system.

- An increase in pump efficiency (from 0.7 to 0.8) results in a 0.15 % decrease in expenditure, which is an economically significant implication.

- The NSGA-II and a Pareto front were utilized in MATLAB software to determine optimal design variables and achieve the best operational conditions. Under optimal operation circumstances, the exergy efficiency and product cost rate were measured at 14.46 % and $74.98/h, respectively.

- NSGA-II demonstrated superior performance, delivering an exergetic efficiency advantage of 0.56 %, 0.46 %, and 0.86 % over PSO, GA, and SA, respectively. Furthermore, it achieved a reduction in cost rate of $1.52/h, $0.82/h, and $2.22/h compared to the aforementioned algorithms.

- The exergoenvironmental research indicated that the Heat Exchanger (HEX) has a high exergoenvironmental factor because it utilizes hot water, which has no exergoenvironmental impact. As a result, there is no environmental damage associated with the destruction of exergy. Pumps have a minor environmental impact in terms of their components, making them essentially zero exergoenvironmental impact factors when compared to other components. The exergoenvironmental parameters were measured for each component, revealing the substantial influence of different components on the total environmental impact of the system.

Future work can focus on a more detailed exergoenvironmental and life cycle analysis of the proposed hybrid system. Additionally, it is recommended to study the conceptual design of the energy system using other types of solar collectors and compare the results. This can greatly assist energy engineers and stakeholders in implementing the optimal system. The limitation of the proposed system is its design for areas adjacent to seawater. However, in regions with suitable solar radiation adjacent to seawater, the proposed system can be a viable option for energy production. It is recommended to conduct a small-scale experimental analysis before implementing the energy system.

Data availability

Data will be made available on request.

CRediT authorship contribution statement

Rahadian Zainul: Validation, Investigation, Formal analysis. Ali Basem: Writing – original draft, Resources, Data curation. Mohamad J. Alfaker: Writing – review & editing, Formal analysis, Data curation. Pawan Sharma: Writing – original draft, Software, Conceptualization. Abhishek Kumar: Software, Resources, Methodology. Mohammed Al-Bahrani: Writing – review & editing, Resources, Data curation. A. Elawady: Writing – review & editing, Resources, Investigation. Mohamed Abbas: Writing – original draft, Methodology. Shatrudhan Pandey: Writing – review & editing, Investigation, Formal analysis. Hadi Fooladi: Writing – original draft, Project administration, Methodology, Formal analysis.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors extend their appreciation to the Deanship of Research and Graduate Studies at King Khalid University for funding this work through Large Research Project under grant number RGP2/411/45
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